Dr Brenda Page, a 32-year-old geneticist based at Aberdeen University, was found dead at her home in the city in July 1978.
The divorcee had been leading a double life, working as an escort to help pay her bills.
The Crown Office said Lord Advocate Frank Mulholland had instructed police to re-investigate the killing.
It follows a review of case papers and an assessment of forensic science “possibilities”.
Detective Superintendent Malcolm Stewart, who will lead the investigation, said: “We’ve been in liaison with Crown Office in terms of the paper review and from that the Lord Advocate has decided that he would like to have it re-investigated.
“The case is from 1978 so there has been significant progress in forensic techniques since that time and one of the things we will be considering is whether the items seized at the time can be subjected to new forensic techniques which may point us in a particular direction.
“That is certainly one aspect of the inquiry we will need to look at closely.”
Ms Page was found murdered in her flat in Allan Street after failing to turn up for work.
The last confirmed sighting of her was when she left the Treetops Hotel in Aberdeen at 2.30am that day after meeting up with two men for dinner.
She drove home alone and was never seen alive again.
Police carried out a major investigation, interviewing about 3,000 people during the inquiry.
However, detectives say there are no suspects at this stage.
Detective Superintendent Stewart said: “It is an opportunity to have a fresh look to carry out a re-investigation, go in with an open mind and see if we can progress it and hopefully get justice for Brenda at the end of it.
“We will need to go and re-interview a number of significant witnesses from the time to see if anybody has thought of anything over the years which they never told the police originally.
“Her next of kin are aware that it is to be re-investigated and are supportive of that and they also hope that we get to the bottom of it.”
Advances in DNA profiling have led to a number of historical cases being reviewed and last year helped lead to the conviction of Angus Sinclair for the notorious World’s End murders in 1977.
Mr Mulholland said Ms Page’s sister, Rita Ling, was pleased that the case was being re-investigated.
He said: “Brenda’s sister is still alive and there has been contact with her to update her on what is happening. It’s been a long time since Brenda’s murder and I think her sister was pleased, but there’s a long road ahead.
“You can never look into the future but I think it is important that you don’t give families false hope so we wouldn’t be doing this unless we had a hope of reasonable possibilities of success here.
“I think it is well worth doing and hopefully it will give confidence to other families in a similar position that these cases are not forgotten about and are periodically looked at with a view to doing what we can to identify the perpetrator and bring him or her to justice.”